Interpolation is the technique of estimating the value of a function for any intermediate value of the independent variable, while the process of computing the value of the function outside the given range is called extrapolation.
Central differences : The central difference operator d is defined by the relations :
Similarly, high order central differences are defined as :
Note – The central differences on the same horizontal line have the same suffix
Bessel’s Interpolation formula –
It is very useful when u = 1/2. It gives a better estimate when 1/4 < u < 3/4
Here f(0) is the origin point usually taken to be mid point, since Bessel’s is used to interpolate near the center.
h is called the interval of difference and u = ( x – f(0) ) / h, Here f(0) is term at the origin chosen.
Input : Value at 27.4 ?
Value at 27.4 is 3.64968
Implementation of Bessel’s Interpolation –
4 -0.154 0.0120001 -0.00300002 0.00399971 -0.00699902 3.846 -0.142 0.00900006 0.000999689 -0.00299931 3.704 -0.133 0.00999975 -0.00199962 3.571 -0.123 0.00800014 3.448 -0.115 3.333 Value at 27.4 is 3.64968
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